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Quantitative Aptitude · Number Series, Coding-Decoding and Odd Man Out

Coding-Decoding: Letter Coding for CA Foundation

Updated 1 October 2026 · Fact-checked

Letter coding replaces each letter of a word with another letter using one fixed rule, such as a forward or backward shift, a mirror letter (positions add up to 27), or a set substitution. Convert letters to positions, find the rule from the given example, test it on every letter, then apply it to the new word.

Understand Coding-Decoding: Letter Coding

In a letter coding question, the paper gives you a word and its coded form. You must find the hidden rule and apply it to a different word. The rule never changes within one question.

Every rule works on the position of a letter in the alphabet. A = 1, B = 2, C = 3 and so on up to Z = 26. Once you turn letters into numbers, a rule becomes simple arithmetic: add a number, subtract a number, or take 27 minus the position.

There are three common rule types. A shift moves every letter by the same number of places (for example +2). A reverse alphabet rule swaps each letter with its mirror (A↔Z, B↔Y, C↔X and so on). A mixed or alternating rule uses different shifts on different positions, such as +1, −2, +1, −2.

The alphabet is a loop. After Z you go back to A, and before A you go to Z. Many wrong answers come from forgetting this.

The skill is not memory. It is spotting the rule from the first one or two letters, then confirming it on the rest. Practise until the positions of common letters come to you instantly.

Key formulas to remember

Letter position
A = 1, B = 2, ... Z = 26
Memorise EJOTY as 5, 10, 15, 20, 25 to find any position fast.
Mirror (reverse) letter
Reverse position = 27 − position
Equivalent check: a letter and its mirror always have positions that add up to 27.
Mirror pairs
A↔Z, B↔Y, C↔X, D↔W, E↔V, F↔U, G↔T, H↔S, I↔R, J↔Q, K↔P, L↔O, M↔N
The middle of the alphabet is between M (13) and N (14).
Forward shift
New position = old position + k
If the result is above 26, subtract 26.
Backward shift
New position = old position − k
If the result is below 1, add 26.
Rule check
Difference = coded position − original position
Find it for every letter. Same difference means a uniform shift. A repeating pattern of differences means an alternating rule.

How to solve Coding-Decoding: Letter Coding questions

Use this same routine for every letter coding question. It takes under a minute once practised.

  1. 1Write the given word and its code one below the other, letter by letter.
  2. 2Write the position number under each letter.
  3. 3Find the difference (coded minus original) for each pair. Ignore signs only if you are sure about direction.
  4. 4Look at the differences. All equal means a fixed shift. Positions adding to 27 means a reverse alphabet rule. A repeating pattern means an alternating rule.
  5. 5Test the rule on every letter of the given example, not just the first.
  6. 6Apply the rule to the new word, one letter at a time, using wrap-around when needed.
  7. 7Match your answer with the options and check it is the only one that fits.

Quickest way: First-letter elimination with a rule check

When to use it: Use it in the exam hall on any four-option letter coding question, especially when the word is long.

  1. Find the rule from the first letter pair only, then confirm it on the second pair.
  2. Code only the first letter of the target word.
  3. Strike out every option whose first letter does not match.
  4. Code the second letter and strike out again. Usually one option is left after two letters.
  5. For a reverse rule, use the sum-27 check: if the two positions add to 27, it is a mirror.
  6. Always check any letter near A or Z for wrap-around before finalising.
  7. If the rule is unclear after about 40 seconds, skip. A wrong answer costs 0.25 marks.

Common mistakes in Coding-Decoding: Letter Coding

  • Forgetting wrap-around past Z or before A

    You treat the alphabet as a line instead of a loop.

    Fix: If a result is above 26, subtract 26. If it is below 1, add 26. For example, A − 2 gives Y.

  • Confirming the rule on only the first letter

    The first letter fits two or three different rules, so you stop early.

    Fix: Test the rule on every letter of the given pair before applying it. Alternating rules show up only from the second or third letter.

  • Using 26 instead of 27 for the mirror letter

    There are 26 letters, so 26 feels natural.

    Fix: The mirror position is 27 minus the position. Check: A (1) and Z (26) add to 27.

  • Counting positions wrongly in the middle of the alphabet

    You count on your fingers and slip by one near L, M, N or O.

    Fix: Anchor on E = 5, J = 10, O = 15, T = 20, Y = 25 and count from the nearest anchor.

  • Coding the target word in the wrong direction

    You find the rule going from word to code but then reverse it, or you mix up coding and decoding.

    Fix: Read the question again. If you are given the code and asked for the original word, apply the opposite operation.

  • Assuming the same shift for every letter

    Most easy questions use a fixed shift, so you stop checking.

    Fix: Write all the differences. If they are not the same, look for a pattern such as +1, −2, +1, −2.

Worked examples

Example 1

If CAT is coded as ECV, how is DOG coded? (a) FQI (b) EPH (c) FPI (d) GQJ

Show the solution
  1. Positions: C = 3, A = 1, T = 20. Codes: E = 5, C = 3, V = 22.
  2. Differences: 5 − 3 = +2, 3 − 1 = +2, 22 − 20 = +2. The rule is a shift of +2 on every letter.
  3. Apply to DOG: D = 4, so 4 + 2 = 6, which is F.
  4. O = 15, so 15 + 2 = 17, which is Q.
  5. G = 7, so 7 + 2 = 9, which is I.
  6. The code is FQI.

Answer: (a) FQI

Example 2

In a certain code, BAT is written as YZG. How is CAR written in that code? (a) XZI (b) XAI (c) XZJ (d) YZI

Show the solution
  1. Positions: B = 2, A = 1, T = 20. Codes: Y = 25, Z = 26, G = 7.
  2. Check sums: 2 + 25 = 27, 1 + 26 = 27, 20 + 7 = 27. So each letter is replaced by its mirror letter (27 − position).
  3. C = 3, so 27 − 3 = 24, which is X.
  4. A = 1, so 27 − 1 = 26, which is Z.
  5. R = 18, so 27 − 18 = 9, which is I.
  6. The code is XZI.

Answer: (a) XZI

Example 3

In a certain code, FIRM is written as GGSK. How is BANK written in that code? (a) CYOI (b) CZOI (c) CYPI (d) DYOI

Show the solution
  1. Positions: F = 6, I = 9, R = 18, M = 13. Codes: G = 7, G = 7, S = 19, K = 11.
  2. Differences: 7 − 6 = +1, 7 − 9 = −2, 19 − 18 = +1, 11 − 13 = −2.
  3. The rule alternates: +1 on odd letters, −2 on even letters.
  4. B = 2, so 2 + 1 = 3, which is C.
  5. A = 1, so 1 − 2 = −1. Add 26 to get 25, which is Y.
  6. N = 14, so 14 + 1 = 15, which is O.
  7. K = 11, so 11 − 2 = 9, which is I.
  8. The code is CYOI.

Answer: (a) CYOI

Exam tips

  • Questions are short and worth the same as any other MCQ, so do them early and quickly to bank easy marks.
  • Always compute the second letter of the target word before choosing, because options often share the same first letter.
  • Watch for wrap-around cases: if the word contains A, B, Y or Z, expect the question to test it.
  • If a question asks you to decode, work backwards from the code with the opposite operation.
  • Skipping saves time, and a wrong answer costs 0.25 marks. A guess after eliminating one or two options has positive expected value, while a pure blind guess is roughly break-even. Use your time wisely and skip only when the rule is unclear.

Practice questions from Number Series, Coding-Decoding and Odd Man Out

Coding-Decoding: Letter Coding: frequently asked questions

What is the reverse alphabet position trick in coding-decoding?

Each letter is replaced by its mirror letter, whose position is 27 minus the original position. So A becomes Z, B becomes Y and M becomes N. A quick check is that the two positions always add up to 27.

How do I know whether the rule is a shift or a reverse?

Find the difference for each letter. If every difference is the same, it is a shift. If every pair of positions adds up to 27, it is a reverse alphabet rule. If the differences repeat in a pattern, the rule alternates.

Do I need to memorise all the letter positions?

It helps a lot, but you only need anchors: E = 5, J = 10, O = 15, T = 20, Y = 25. Count forward or back from the nearest anchor. With practice, most positions come automatically.

How much time should I spend on one coding-decoding question?

Aim for under a minute. If you cannot spot the rule in about 40 seconds, move on and return later if time remains. Skipping saves time, and a wrong answer costs 0.25 marks. A guess after eliminating one or two options has positive expected value, while a pure guess is roughly break-even, so skip only when the rule is unclear.